Simulator



May 7,' 1957 R. G. PIETY I SIMULATOR Filed Jan. 2. 1953 30 la? 7 2" z5 l' I r I I; o 'c 26 4 Sheets-Sheet 1 INVENTOR.

gyn. l. Hw* www A TTRNEYS R. G. PIETY SIMULATOR May 7, 1957 4 Sheets-Sheet 2 Fild Jan. 2, 1953 4 Qwm INVENTOR.

R. G. PIETY May 7, 1957 SIMULATOR 4 Sheets-Sheet 3 Filed Jan. 2, -1953 May 7, 1957 R. G. Pil-:TY 2,791,375

SIMULATOR K Filed Jan. 2, 1955 4 sheets-sheet 4 AMPLIFIER A fr om/f ya States Patent'Oflice Patented May 7,' 1957 SIMULATOR Raymond G. Piety, Bartlesville, Okla., assignor to Phillips Petroleum Company, a corporation of Delaware Application January 2, 1953, Serial No. 329,279

12 Claims. (Cl. 23S-61) This invention relates to a simulator which is a mechanical analogue of a pumping system. In one specific aspect it relates to a simulator which is a mechanical analogue of the tubing, sucker rod, oil column, and pump in a deep well pumping unit.

A typical l,deep well pumping system includes a series or string of metal rods, referred to i-n the art as sucker rods, which extend through tubing positioned in the well, the lower end of which carries a pumping unit. The tubing, in turn, is suspended Within a Well casing and, under some conditions, the lower portion of the interspace between the tubing :and casing may contain a column of oil. At the top of the well, the sucker rod string extends through a stuiing box and is driven by a prime mover, such as an electric motor or an inter-nal combustion engine, through :a flywheel or bull wheel. The flywheel, in turn, drives a crank or counterbalance which is coupled through a walking beam to the top end of the sucker rod string.

As the pumping operation is carried out, a column of oil rises in the region between the tubing and the sucker rod string, thus producing a viscous drag upon both the tubing and sucker rod string. The weight and elasticity of the sucker rod string, as well as the tubing and oil column, produce elastic strains in the pumping unit so that the sucker rod string and tubing behave in a manner somewhat'analogous to elongated springs.

This elastic movement of the sucker rod string and tubing oftentimes results in failure of one or more sucker rods and, more often, in ineiiicient operation of the pumpingv system. It has not been possible, in" the past, to predict the eliect of changes in various operating variables of the system with any `degree of' accuracy, except'by purely empirical or cut and try methods, for the obvious reason that the movement of the sticker rod string several miles below the surface of the earth cannot be obsewed nor is it possible to observe the manner of operation of the downhole pump.

It has been proposed to construct a mechanical model of the pumping system so that adjustments of various operati-ng variables of the scale model would produce effects-thereon similar to the eifects of changes in corresponding Variables upon the :actual pumping system. Unfortunately, to obtain any useful results by such a system, it can be demonstrated mathematically that the scale model itself would be of such large size and prohibitive cost as to render construction thereof entirely impractical. However, it has been discovered in accordance wit-h the present invention that a mechanical analogue of' la pumping system can be established on a practical scale. In this analogue system a series of weights is connected in spaced relation on three lines representing, respectively, the oil column, the tubing, and the sucker rod string. The three lines are exibly coupled by damping members which represent the viscous drag .of the oil vcolumn on both the tubing and sucker rod string. The forces tending to displace the various weights from their normal positions represent stresses imposed upon corresponding elements of the sucker rod string, tubing and oil column, while the velocities and displacements of the weights represent the velocities and displacements of corresponding parts of the pumping unit. In corresponding fashion, other parameters of the analogue or mechanical system represent corresponding variables and constants of the prototype pumping unit.

Accordingly, it is an object of this invention to provide a mechanical system which is an analogue of an actual well pumping unit, which system may be utilized to predict the effect of changing various operating conditions of the pumping system.

It is a further object to provide apparatus of the type described which is simple to construct, reliable in operation, and which employs a minimum number of inexpensive components.

Various other objects, advantages and features of the invention will become apparent from the following detailed description taken in conjunction with the accompartying drawings, in which:

Figure l is a vertical sectional view, partially in elevation, of a typical deep well pumping system;

Figure 2 is a schematic view of the analogue system simulating the operation of the deep well pumping unit;

Figures 3, 4, 5, 6, and 7 are diagrammatic views illustrating features of this invention;

Figure 8 illustrates apparatus employed to couple viscously the various lines of the analogue system;

Figure 9 illustrates apparatus simulating the downhole pump; and

Figure l0 is a schematic representation of the analogue surface pumping unit and indicating system.

Referring now to Figure l, there is illustrated, in a schematic manner, a typical deep well pumping system to which the simulator of this invention is applicable, this system including a driving mechanism 10 located at the surface and a downhole pumping unit 11. Unit 11 includes the usual well casing 12 within which is mounted a tubing 13 having a sucker rod string 14 suspended therein, the latter including 1a number of sucker rods 15 connected together by joints 16. The upper end of string 14 extends through aV stuiling box 1'7 in a casingV head 18 and the lower end is attached to a plunger 19 forming a part of a pump 20 which includes an upper or traveling valve 21 and a bottom or stationary valve 22.. The uppermost sucker rod or polished rod 23 is driven by mechanism 10 which includes a Walking beam 24 secured at one end to the polished rod. and at its other end to a pitman 25 which is driven by a crank or counter-balance 26. Crank 26 is driven by a ilyv/heel 27, as through a chain drive 2S; and flywheel 27, in turn, is driven by a prime mover 29, as by a second chain drive 3l). Prime mover 29 may be an electric motor, an internal combustion engine, or any other suitable type of engine.

-In accordance with this invention, the operation of the downhole unit l1 is mechanically simulated by the apparatus of Figure 2. The displacement forces on various members ofthe analogue system represent stresses on corresponding parts of the pumping unit, the displacements of var-ions members of the analogue system represent displacements of corresponding parts of the actual pumping system, and velocities in` the analogue system represent the velocities of corresponding parts of the mechanical system. In order for the two systems to be analogues of one another, it is necessary that the equationspdescribing the behavior of the analogue system be similar t-o the equa-tions describing `the behavior of the actual pumping unit. Thereupon, by suitably adjusting the coetcients of various terms of the analogue system,

as by changing the parameters of various parts of the analogue system, a condition is obtained whereby the displacement forces, displacements, velocities and other parameters of the analogue system correspond to the stresses, displacements, velocities and other related variables of the pumping unit. At this time, the two systems are analogues of one another and further changes in the parameters f the analogue system produce effects thereon which enable accurate prediction of the eiects of corresponding changes in the pumping unit.

In the simulator of Figure 2, a line T represents the tubing 13, a line O represents the oil column, and a line R represents the sucker rod string 15. These letters are employed throughout the following description as subscripts to represent the line t0 which they are applicable, such as the tubing, oil or rod line. The following notation is used in the equations to be derived which define the motion of the two systems:

Pumping System Analogue System l-length of sucker rod, oil column, or tubing segment.

qxl-compression in oil column segment.

er, co, et-elastic modulus of the sucker rod, oll column, and

tubing, respectively.

sr, 3, .ii-cross sectional area of sucker rod, oil column, and

g-gravity constant.

Ict-viscosity constant relating to movement between sucker rod and oil column segments.

Ito-viscosity constant relating to movement between oil column and tubing segments.

tubing segments, respectively.

tubing segments, respectively.

d-distance between adjacent sucker rod, oil column, or tubing weights.

Xi, Yi, Zj-displacement of sucker rod, oil colunm, and tubing weights, respectively.

W, L, M-Weight of sucker rod, oil column, and tubing weights, respectively.

Ui, Vi, i-veloclty o sucker rod, oil column, and tubing weights, respectively.

ai, j, :5i-acceleration ot sucker rod, oil column, and tubing weights, respectively.

A., At-tension in sucker rod and tubing lines, respectively.

rta-tension in oil column line.

Kil-viscosity constant relating to movement between sucker rod and oil column weights.

Kif-viscosity constant relating to movement between tubing and oil column weights.

ki--viscosity constant relating to movement between tubing segments and fluids outside the tubing.

lIn the mathematical analysis of the pumping unit and -analogue system which follow, the respective equations are derived by the method of nite differences. In accordance with this method the casing, tubing, and sucker rod string are divided into a large number n of segments. During the operation of the pumping unit each segment of the sucker rod, tubing, and oil column moves upward or downward in accordance with the mechanical laws governing the system, It has been discovered that corresponding equations describe the motion of the weighted line analogue system.

In particular, considering the nth segment 34 of the sucker rod, as defined by the dotted lines 32 and 33, Figure 3, let it be assumed that at a given instant the lower end of this nth segment is displaced downward from its equilibrium position `a distance xn and the upper end of the segment is displaced downward from its equilibrium position la distance x11-1. This displaced position is represented by 34'. Such a displacement results in a stretching of the nth segment by an amount xn-xn-r, which in turn results in a strain :vn-u-l l so that the total stress in the nth seg-ment becomes:

4 In like manner a corresponding equation can be written for the (n+1)th segment as follows:

both above and below the nth station, Figure 3. Segment 34 has acting upon it a total tension pn+1 on its bottom end, a tot-al tension pn on its top end, the aforementioned upward viscous drag, and `a downward weight wrl. The resultant force produces a downward acceleration an at the mid-point of the segment in accordance with equation:

The basic sucker rod equation is realized by combining lEquations l, 2, and 3 to obtain:

Srer l Equation 4 has itscounterpart in the analogue system of Figure 2. This analogue system comprises three lines R, T, :and O representing, respectively, sucker rod string 14, tubing 13, `and the oil column between tubing I13 and string i14. Lines R, O, and T preferably are constructed of an electrically conductive material such as -steel wire, and each is anchored at one end to a support f member 40. The second ends of `lines R, O, and T pass over a bar 41 and have respective weights 42, 43, and 44 attached thereto to provide respective tensions Ar, A0, and At in the lines. A Iseries of weights W is secured to line R in spaced relationship Ias -by -set screws 45, and corresponding weights Lv and M are secured in like man- H ner to respect-ive lines O and T adjacent corresponding weights W. Each of the adjacent weights W and L is viscously coupled to the other as are adjacent weights L and M. fI'hi-s coupling is provided by` a series of devices 49, one of which is illustrated in detail in Figure 8. A pan 50 iilled with a liquid 51, such as oil, is secured to weight WJ and a plate 52 is secured to an adjacent weight Ln so as to Ibe free to move back and forth in liquid 51 whenever weights Wj and LJ are moved relative to one another. Each of the weights W, L, and M, pans 50 and plates 52 is suspended by suitable lines 55 from an overhead support 56. In this manner the downward force of gravity exerted on the various members `of the analogue system is eiectively eliminated, the -importance of which is brought out in the equations that follow. A drive mechanism 58 is connected to the W weight nearest support 40 to impart a reciprocating motion thereto representative of the pumping unit 10, land a stepless pawl mechanism 59 is connected between the W and L weights nearest bar 41 to represent the reacting forces exerted by the downhole pump assembly 20. Mechanisms 58 and 59 are described in greater detail hereinafter.

With reference to Figure 4 let it `be assumed that sucker rod line R designates a line whose mass can be neglected which is under a tension Ar. Line R is loaded at intervals d with equal Weights W not under the influence of gravity. Let it further be assumed that at a given instant the line is disturbed as illustrated wherein the various X values represent the displacements of corresponding Weights W from their normal positions along dotted line 60. These displacements are greatly exaggerated for purposes of illustration. If the X displacements are small,` however, the tensions on the individual line segments remain substantially equal to the applied tension An Figure 5 illustrates diagrammatically the `forces exerted on weight Wj. The net force Fj which tends to displace weight W1 normally to line 60 is equal to the difference between displacement force FJ and restoring force F3, that is:

For small displacements sin and. lsin qt ure equal to tan 0 and tan qt, respectively, andtos the respective angles 0 and p expressed in radians, such that Equation 5 becomes:

eexia-exfifxf-u 6 Force F3 is made up off-a'dynarn-ic reaction and a viscous loading; term Kr(U-4-.V1), assuming weights Wjand: L1 aretmoving apart, such that Equation 6 becomes:

A comparison of Equations 4 and 7 reveals that they are analogous term by term, except that the last term of Equation 4 is missing from Equation 7. Howe-ver, because this missing term represents the static load created by the mass of the sucker rod it can be neglected for purposes of analysis. The important quantity under consideration is the variation in excess loading over the static yvalue. lIn view of the analogy between Equations 4 and 7 it ybecomes evident that a study of various quantities such as displacements, velocities. and forces affecting the simulator vibrating line R will provide information regarding corresponding quantities in the prototype sucker rod string.

Similar equations can ybe derived with respect to the compressive stress on the individual segments ofA the oil column and the motion of a gener-al segmentl of the oil column. With reference 'to Figure 6,V consider-ing the nth segment y64 of the oil column as defined by the dotted =lines `62 and 63, 'let it 4be assumed that at a given instant the lower end of this nth segment is displaced downward from its equilibrium position a distance yn and that the upper end of the segment is displaced` downward :from its equilibrium posit-ion a distance yn-i. This displaced position is represented by 64. Such a displacement results in a compression of` theA nth seg;- ment by an amount yn-yn-i, whichy in turn results in a strain so `that the: total compressive stress in the nth segment is v q 6V Y In like manner a corresponding equation can be written for 'the (n+11)th segment as Ifollows:

se q+1= (ynl yn) (9) The equation of motion of the oil column segment 64 which extends a distance The lbasic oil column equation is realized by combining Equations 8, 9, and l0 to obtain:

f -lb sz'e(y+1-2y+y1) -w-"gl-lkrl.(unf`i"vn)`i`kl(vn+n) wel Equation 1,1 also has its counterpart; in the analogue system ofi Figure. 2. The equation of motion of the vibrating weights L corresponds to Equation 6 and can be written as -followsz =Force G5 is made up of a dynamic reaction a first lviscous -loading term Kr(U9-{V,-) and a second viscous loading term. KAI/H41) such that Equation 12 becomes:

A comparison of Equations 11 and 13 reveals that they are analogous term byV term except that the last term of Equation 11 is missing from Equation 13. However, since this missing term represents the static load created by' the mass of the oil column it Ican also be neglected in the analysis. In View of the analogy between Equations `ll and' I3 it becomes evident that line O simulates the action of the oil column in the pumping system.

The movement of the tubing is governed generally bythe same equations as the movement of the sucker rod. With reference to iFigure 7, considering the nth segment 74 ofthe tubing as defined Aby the dotted lines 72 'and 73', 'let it be, assumed that at a given instant the lower end of this nth segment is displaced downward from its equilibrium position a distance zn and the upper end of the segment is displaced downward from its equilibrium position a distance zn-i. This displaced position is represented by'74'. Suchv a displacement results in a stretching of the nth segment by an amount zn-znan which in turn results in a strain KStVeZn-Znrl):

Pn l

l'l' In like manner a corresponding equation can be written lfor the (n+1)th segment as follows:l

The equation of motion of the tube segment 74", which extends a distance The basic tubing equation is realized by combining Equations 14, l5, and 16 to obtain:

Equation 17 also has its counterpart in the analogue system of Figure 2. The equation of motion of the vibrating weights M corresponds to Equation 6 and ca n be written as follows:

Force HJ is made up of a dynamic reaction IVI-i;

and a viscous loading term K0(V1+I1) such that Equation 18 becomes:

A comparison of Equations 17 and 19 reveals .that they are analogous term 'by term except that the last two terms of Equation 17 are missing from Equation 19. However, since this last missing term represents the static load created by the mass of the tubing it can also be neglected in the analysis as can the next to the last term because in is negligible. In view of the analogy between Equations 17 and 19 it becomes evident that `line T simulates the action of the tubing in the pumping system.

From the foregoing description, -it will 'be evident that the simulator illustrated in Figure 2 is an analogue of the pumping system of Figure l. The actual pumping system obviously can be divided into Ias many segments as desired, each such segment being represented by a corresponding set of weight-s W, L, and M in the apparatus of Figure 2, the accuracy becoming greater with an increasing number of Segments.

As stated, the vibrating weight system thus far described simulates the sucker rod string together with its associated cil column and tubing. ing string is anchored at the surface so that it must remain stationary, that is, its di-splacement must vbezero at all times. This condition is represented-in Figure 2 by anchoring the top weight M to bracket 79 to prevent vibration thereof.

The prototype sucker rod string is driven at its top end Aby drive mechanism which includes the prime mover, flywheel, crank and walking beam of Figure 1. For present purposes, it is assumed that the reaction of the sucker rod system upon the'Adrive mechanism is The top of the tub-V negligible, which is true in certain practical applications and Where results are desired only to a predetermined degree of accuracy, 'so that the motion at the top end of the sucker rod string can be expressed as a sinusoidal function. lIn the illustrated embodiment of this invention, such ldriving motion is imparted to the sucker rod line by the mechanism 68 lshown in Figure 10. -An electric motor 80 is connected 4through a speed reducing gear train 81 to a rotatable disk A32. An arm 83 is pivotally connected at yone end to disk 82 and at its other end to one end of a rod 8'4 which is constrained by guides 85 for axial movement. The other end of rod 84 is connected to the uppermost weight W of line R. -From an inspection of Figures 1 and 10 it can be seen that motor 80, gear train '81, disk 82, arm 83 and rod 84 simulate, respectively, engine 29, cable S10-wheel 27-cable 28, crank 246, pitman 25 and walking beam 24 of the prototype pumping system.

A mechanical device known as a stepless pawl is em-:

ployed to simulate the action of the valve and pump assembly disposed in the lower region of the bore hole.

This stepless pawl is shown diagrammatically in Figure 9 as comprising a pair of rotatable pulleys 90 and 91 which are mounted on a common shaft 9.2. A third pulley 94 is mounted on a shaft 95 which in turn is connected' by a f yoke 96 to the oil column line O. An inextensible cable 98 is connected at one end to the sucker rod wire R at a weight W. Fromv wire R, cable 98 circles pulley 90, thence around pulley 94 back laround pulley 91 and is `finally secured to an anchor post 99. VA weight 100 is fastened to oil column wire O by means of a cable 101 which passes over a tixed pulley =102.

Weight serves to maintain a tension at points 105 and 106 in cable 98. When the sucker rod wire moves away from this assembly tension appears at point 108 and slack at point 109. When the sucker-rod wire moves toward the assembly, Vslack appears at point 108 and tension at point 109. Under the first condition pulleys 90 and 91 rotate in the clockwise direction indicated by the arrow. Under the second condition the cable slips over pulley 90 and both pulleys 90 and 91. are held sta tionary because there is tension in the cable on both sides of pulley 91 at points 106 and 109. This action isI analogous to that of the pump assembly at the bottom of the sucker rod string. On the upstroke, oil is lifted by the pump plunger and on the downstroke the oil is held stationary by the check valve. In the stepless pawl assembly the rotation of pulleys 90 and 91 is intermittent Iand in one direction only. Accordingly, the total rotation of these pulleys is a measure of the total quantity of oil produced. This rotation can be determined visually by positioning a suitable scaley 110 adjacent a pointer 111 on pulley 90, or the rotation can be recorded through suitable mechanical or electrical linkage well known in the art. The oscillatory motion imparted to the oil column wire is through this stepless pawl assembly analogous to the compressional waves set up in the oil column by the pump action in the prototype system.

The only points in the surface pumping system that are conveniently accessible for making measurementsr dynamometer card are obtained in accordance with this A invention. With reference to Figure 10, a stress responsive element 115 is shownas being mounted between disk 82 in the driver assembly and vsucker-rod line R. Elemenare 9 Y. ment 115 can be a carbon microphone buttton or a strain gage. Voltage source 116 is connected in series therewith. The tension on element 115 varies its electrical resistance in a manner which is proportional to the force applied to the sucker-rod wire. The resulting voltage signal is amplied by a suitable amplifier 117 and applied to the vertical detlection plates of a cathode ray oscilloscope H9 to provide the force axis. The displacement axis is obtained through a capacitive pickup. A high frequency electrical signal, 1Q kilocycles for example, is applied to the conductive sucker-rod wire R by an oscillator 120. Each of the metallic loading weights W can thus be employed as one plate of a pickup condenser. ln order to simulate the polishedrod dynamometer card the weight W nearest the surface unit is selected. The second plate of the pickup condenser is in the form of a metallic plate 121 mounted directly under weight W. The opposing area presented by the two plates to one another therefore varies as the weight W oscillates. Accordingly, the amplitude of the electrical signal picked up bythe capacitor plate 121 varies as the displacement of theV driving point weight W. The output of the pickup is amplified and demodulated by a conventional circuit 123 to provide an electrical signal, the amplitude of which is representative of the displacement of the sucker-rod lineweight W. This demodulated signal is applied to the horizontal del'ecting plates of oscilloscope 119 to provide the displacement axis.

T he simulator of this invention thus provides a means for analyzing the behavior of a sucker-rodV pumping system when the operating conditions and the actual dynarnometerV measurements of the polished rod are known. The simulator constants and scale factors first are determined from the prototype system constants and operation conditions, that is, the various terms such asfW, Ar and d, for example, are calculated from the known rodr and tube sizes, oil density and pump stroke rateof the actual pumping system. The valve and p ump operation thenj is varied until the signal provided by oscilloscope 11.9;

corresponds to the actual dynamometer card ofthe polished rod. Such a correspondence can be obtained by varying the speed of operation of the pump unit. When the simulator and previously determined 'dynarnometer measurements correspond to one another, the behavior of the vibrating loaded lines can be observedl and the motion of the loading weights recordedu through the u se of the capacitive pickups similar to that used to generate the polished` rod displacement axis. In this manner thel behavior of the downhole portion of the system can be studied and the type of behavior responsible for the various characteristic features ofthe dynamometer measurements cank be determined. Furthermore,v optimum operating conditions forthe prototype pumping system canbe determined by this same means and a dynamometer pattern derived which whenv obtained b y the prototype pumping system assures such optimum conditions of operation.

As illustrated in Figure 2, the vibrating system of the simulator is suspended from a plurality of support wires S5. These support wires should be attached to the weights and viscous coupling devices at their centers of percussion in order to prevent rotation of these members about the suspending wires. lt is believed evident that extreme care must bev taken to prevent extraneous vibrations from entering, thev simulator system. In this respect it is important to avoid any loose, construction in thedrive mechanism. Wires R, O, and, T should havea maximum ilexibility, that-is, a4 low' resistance to bend-` ing. lt also is importanty that such wires have a rela,- tively high` tensile strength.

While this invention has beenl described in conjunction with a present preferred embodiment thereof, it is to be understood that this description is illustrative only and is not intended to limit the invention because various 10 details of construction obviously can be modied within the scope of the invention.

What is claimed is:

l. Apparatus for simulating a downhole pumping system including a sucker rod string, tubing surrounding said sucker rod string, and an oil column between said rod and said tubing comprising three flexible lines disposed in generally parallel horizontal relationship, means to apply predetermined tensions to said lines, a plurality of weights attached to each of said lines in spaced relation, said weights being constrained for movement inv a horizontal plane, each individual weight representing, respectively, a sucker rod segment, an oil column segment and a tubing segment, means viscously coupling the individual weights representing the sucker rod segments to adjacent individual weights representing the oil column segments to simulate the actual viscous drag between adjacent rod segments and oil segments, means viscously coupling the individual weights representing the tubing segments to adjacent individual weights representing the oil column segments to simulate the actual viscous drag between adjacent tubing and oil -column segments, and means to impart transverse reciprocating motion to the line representing the sucker rod string to simulate the pumping unit driving the uppermost sucker rod'.

2. The combination in accordance with claim l wherein each of said coupling means comprises a liquidfilled pan secured to one of said weights and a plate secured to an adjacent weight and extending therefrom into said pan whereby relative motion between adjacentV weights results in movement of said plate through the liquid in said pan tocreate a viscous drag between said pan and said plate.

3. Apparatus for simulating a downhole pumping system including a sucker rod string, tubing surroundingsaid sucker rod string, an oil column between said rod and said tubing, a pumping unit driving the uppermost sucker rod, and a downhole pump driven by the lowermost sucker rod comprising three ilexible lines disposed in generally parallel horizontal relationship, means to apply predetermined tensions to said lines, a plurality of Weights attached to each of said lines in spaced relation, said weights being constrained for movement in a horizontal plane, each individual weight representing, respectively, a sucker rod segment, an oil column segment and a tubing segment, means viscously coupling the individual weights representing the sucker rod segments to adjacent individual weigllts representing the oil column segments to simulate the actual viscous drag between adjacent rod segments and oil segments, means viscously coupling the individual weights representing the tubing segments to adjacent individual weights representing the oil column segments to simulate the actual viscous drag between adjacent tubing and oil column segments, means to impart transverse reciprocating motion to one end of the line representing the sucker rod string to simulate the pumping unit driving the uppermost sucker rod, and means to measure motion of the second end of the line representing the sucker rod string which simulates the laction of the downhole pump driven by the lowermost sucker rod.

4. The combination in accordance with claim 3 wherein said means to impart reciprocating motion to the line representing the sucker rod string comprises a rod attached at one end to said one end of said sucker rod line,` said rod being constrained for linear movement, -a motor having a drive shaft mounted on a stationary base and disjjiosedv to rotate said drive shaft, a crank arm disposed to be rotated by said drive shaft, and la pitman coupling said crankarm and said rod, whereby reciprocating motion is imparted to said sucker rod line.

5. The combination in accordance with claim 4 further comprising anr electrical resistance strain responsive element secured to` said rod, a source of electrical energy connected in circuit with said strain responsive element,

and circuit means to establish a voltage proportional to the stress on said strain responsive element.

6. The combination in acordance with claim 3 wherein said means to measure motion of the line representing the sucker rod string comprises first and second pulleys mounted on a common rotatable shaft, a third pulley having its shaft connected to the line representing the oil column, a rigid support, an inextensible line secured at one end of the line representing said sucker rod string, said incxtensible line circling said first pulley, said third pulley, and said second pulley in the order stated and being connected at its second end to said support, tension supplying means connected to the shaft of said third pulley to retain said inextensible line under tension, and means to measure rotation of said first 4and second pulleys which simulates the quantity of oil pumped.

. 7. Apparatus for simulating the action of a pump positioned in a bore hole and driven by a sucker rod string extending to the surface of the bore hole comprising a. pair of horizontal lines simulating respectively the sucker rod string and the column of oil pumped to the surface within the well tubing, means to impart reciprocating motion to said sucker rod line transversely of said line to simulate the pump driving the uppermost sucker rod, first and second pulleys mounted on a common rotatable shaft, a third pulley having its shaft connected to the oil column line at the end thereof which represents the bottom of the bore hole, a rigid support, an inextensible line secured at one end to the second end of said sucker rod line, said inextensible line circling said first pulley, said third pulley, and said second pulley in the order stated and being connected at its second end to said rigid support, means to apply a tension to the shaft of said third pulley to retain said inextensible line under tension, and means to measure rotation of said first and second pulleys which simulates the quantity of oil pumped.

8. Apparatus for simulating a down-hole pumping systern including a sucker rod string, tubing surrounding said sucker rod string, an oil column between said rod and said tubing, and a pumping unit driving the uppermost sucker rod comprising three flexible lines disposed in generally parallel horizontal relationship, means to apply predetermined tensions to said lines, a plurality of weights attached to each of said lines in spaced relation, said weights being constrained for movement in a horizontal plane, each individual weight representing, respectively, a sucker rod segment, an oil column segment and a tubing segment, means viscously coupling the individual Weights representing the sucker rod segments to adjacent individual weights representing the oil column segments to simulate the actual viscous drag between adjacent rod segments and oil segments, means viscously coupling the individual weights representing the tubing segments to adjacent individual weights representing the oil column segments to simulate the actual viscous drag between adjacent tubing and oil column segments, means to impart transverse reciprocating motion to one end of the line representing the sucker rod string to simulate the pumping unit driving the uppermost sucker rod, and means to measure the motion of any selected weight which represents the motion of the corresponding segment simulated thereby.

9. The combination in accordance with claim 8 wherein said last mentioned means comprising a source of electrical energy applied to said selected weight whose motion is to be measured, said selected weight being constructed of an electrically conductive material having a first plane surface, a body of electrically conducting material having a second plane surface disposed adjacent and parallel to said first surface thereby forming a condenser therewith, and means to measure the potential induced on said second surface, said potential representing the area of said second surface overlapped by said tirst surface, and thereby the distance said selected weight is displaced.,.`

10. Apparatus for simulating a downhole pumping system including a sucker rod string, tubing surrounding said sucker rod string, an oil column between said rod and said tubing, a pumping unit driving the uppermost sucker rod, and a downhole pump driven by the lowermost sucker rod comprising three flexible lines disposed in generally parallel horizontal relationship, means to apply predetermined tensions to said lines, a plurality of weights attached to each of said lines in spaced relation, said weights being constrained for movement in a horizontal plane, each individual weight representing, respectively, a sucker rod segment, an oil column segment and a tubing segment, means viscously coupling the individual weights representing the sucker rod segments to adjacent individual weights representing the oil column segments to simulate the actual viscous drag between adjacent rod segments and oil segments, means viscously coupling the individual weights representing the tubing segments to adjacent individual weights representing the oil column segments to simulate the actual viscous drag between adjacent tubing and oil column segments; means to impart transverse reciprocating motion to one end of the line representing the sucker rod string to simulate the pumping unit driving the uppermost sucker rod comprising a I rod attached at one end to said one end of said sucker rod line, said rod being constrained for linear movement, a motor having a drive shaft mounted on a stationary base and disposed to rotate said drive shaft, a crank arm disposed to be rotated by said drive shaft, and

t a pitman coupling said crank arm and said rod, whereby reciprocating motion is imparted to said sucker rod line; and means to measure motion of second end of the line representing the sucker rod string which simulates the action of the downhole pump driven by the lowermost sucker rod comprising first and second pulleys mounted on a. common rotatable shaft, a third pulley having its shaft connected to the line representing the oil column, a rigid support, an inextensible line secured at one end to the line representing said sucker rod string, said inextensible line circling said first pulley, said third pulley, and said second pulley in the order stated and being connected at its second end to said support, tension supplying means connected to the shaft of said third pulley to retain said inextensible line under tension, and means to measure rotation of said first and second pulleys which simulates the quantity of oil pumped.

1l. The combination in accordance with claim 10 wherein each of said coupling means comprises a liquid filled pan secured to one of said weights and a plate secured to an adjacent weight and extending therefrom into said pan whereby relative motion between adjacent weights results in movement of said plate through the liquid in said pan to create a viscous drag between said pan and said plate.

l2. Apparatus in accordance with claim 10 further comprising an oscilloscope, an electrical resistance strain responsive element secured to said rod, a source of electrical energy connected in circuit with said strain responsive element, and circuit means to establish a voltage proportional to the stress on said strain responsive element, said voltage being applied to one set of deflection plates of said oscilloscope, a second source of electrical energy applied to the particular weight on said line representing the sucker rod string representing the uppermost sucker rod segment, said particular weight being constructed of an electrically conductive material, a plate of electrically conducting material positioned adjacent said particular Weight thereby forming a condenser with said particular weight, and means to apply the voltage induced on said plate to the second set of vdeflection plates of said oscilloscope whereby the output of said oscilloscope simulates the combined forces ou and displacements of the uppermost of said sucker rod segments.

No references cited. 

1. APPARATUS FOR SIMULATING A DOWNHOLE PUMPING SYSTEM INCLUDING A SUCKER ROD STRING, TUBING SURROUNDING SAID SUCKER ROD STRING, AND AN OIL COLUMN BETWEEN SAID ROD AND SAID TUBING COMPRISING THREE FLEXIBLE LINES DISPOSED IN GENERLLY PARALLEL HORIZONTAL RELATIONSHIP, MEANS TO APPLY PREDETERMINED TENSIONS TO SAID LINES, A PLURALITY OF WEIGHTS ATTACHED TO EACH OF SAID LINES IN SPACED RELATION, SAID WEIGHTS BEING CONSTRAINED FOR MOVEMENT IN A HORIZONTAL PLANE, EACH INDIVIDUAL WEIGHT REPERSENTING RESPECTIVELY, A SUCKER ROD SEGMENT, AN OIL COLUMN SEGMENT AND A TUBING SEGMENT, MEANS VISCOUSLY COUPLING THE INDIVIDUAL WEIGHTS REPRESENTING THE SUCKER ROD SEGMENTS TO ADJACENT INDIVIDUAL WEIGHTS REPRESENTING THE OIL COLUMN SEGMENTS TO SIMULATE THE ACTUAL VISCOUS DRAG BETWEEN ADJACENT ROD SEGMENTS AND OIL SEGMENTS, MEANS VISCOUSLY COUPLING THE INDIVIDUAL WEIGHTS REPRESENTING THE TUBING SEGMENTS TO ADJACENT INDIVIDUAL WEIGHTS REPERSENTING THE OIL COLUMN SEGMENTS TO STIMULATE THE ACTUAL VISCOUS DRAG BETWEEN ADJACENT TUBING AND OIL COLUMN SEGMENTS, AND MEANS TO IMPART TRANSVERSE RECIPROCATING MOTION TO THE LINE REPRESENTING THE SUCKER ROD STRING TO STIMULATE THE PUMPING UNIT DRIVING THE UPPERMOST SUCKER ROD. 